Question

Hey there Could you plz help me id appreciate it so much: ) LIMITED TIME

Answer 1

The independent variable is known as 'x', and the dependent variable is known as 'y'. They just changed the variables here 'f(t)' or 'f(x)' is the same thing as 'y', and 't' is the same thing as 'x'.

So 't' is the independent variable, and 'f(t)' is the dependent variable.

The wording of the second option, the second to last, and the last is all correct. The questions says "let 't' be the time in years after 2000", so if 't' were say 5, this would mean 5 years after 2000 or 2005.  The question also states "let f(t) be the amount of garbage", so the result must be the amount of garbage.

So now we just need to confirm if the calculations were done correctly.

Option 2:

$\sf f(2)=1233$

This is the same thing as saying if you plug in 2 for 't', you will get 1233, let's try it:

$\sf f(t)=1200\cdot (1.05)^t$

Plug in 2 for 't':

$\sf f(2)=1200\cdot (1.05)^2$

Simplify the exponent:

$\sf f(2)=1200\cdot (1.1025)$

Multiply:

$\sf f(2)=1323$

So option 2 is incorrect, and we see also that option 6 is correct. Now for the last one:

Option 7:

$\sf f(4)=1458.6$

This is the same thing as saying if you plug in 4 for 't', you will get 1458.6, let's try it:

$\sf f(t)=1200\cdot (1.05)^t$

Plug in 4 for 't':

$\sf f(4)=1200\cdot (1.05)^4$

Simplify the exponent:

$\sf f(4)=1200\cdot (1.21550625)$

Multiply:

$\sf f(4)\approx 1458.6$

So the last option is also correct.

So your answers are options 3, 4, 6 and 7.